Methods and Systems for Disease Classification

ABSTRACT

This invention describes methods and systems for use of computer vision systems for classification of biological cells as an aid in disease diagnostics. More particularly the present invention describes a process comprising employing a robust and discriminative color space which will help provide segmentation of the cells; employing a segmentation algorithm, such as a feature-based level set, that will be able to segment the cells using a different k-phase-segmentation process, which detect for example, if a while blood cell occurs for segmenting the internal components of the cell robustly; employing a combination of different type of features including shape, texture, and invariant information, and employing a classification step to associate abnormal cell characteristics with disease states.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. §119 of U.S.Provisional Application Ser. No. 61/967,316, filed on Mar. 17, 2014,which is incorporated by reference herein in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

Not Applicable.

BACKGROUND OF THE INVENTION

The field of the invention relates generally to disease diagnostics.More particularly, the invention relates to methods and systems foranalyzing images of biologic cells to aid in identifying and classifyingdisease. In one embodiment of the present invention, the color space ofan image of blood cells is transformed to create an alternatepresentation of the image that more clearly identifies pathologic cells.

Pathology is an essential tool used in the diagnosis of variousdiseases. Typically, a licensed pathologist will observe a biologicalsample under a microscope to make a determination of whether a diseaseis present in the patient. The diagnosis is dependent on the skill andexperience of the pathologist, the stage of disease progression, and thequality of the image captured. While pathology is commonly used, it isrelatively expensive compared to other medical costs and not readilyordered in the early stages of a disease. For example, a patient who hasdeveloped cancer may exhibit symptoms consistent with more commondiseases, such as the flu. Only when the patient has not responded totreatment of the symptoms might a treating physician perform a tissueanalysis. However, in the example of a cancer patient, early detectionimproves the chance of success for treatment. In addition, thepathologist has a limited ability to quantify the abnormalities presentin a sample, which could be critical in borderline cases.

To overcome these limitations, a number of approaches have been taken toperform computer vision-based and machine learning-based analysis ofbiologic cells as an aid in disease diagnostic. These methods seek tosegment, or isolate, cell populations as a first step, then classifyindividual cells through further analysis as being abnormal orindicative of a disease. To perform computer vision-based analysis,various parameters of the image, such as color, intensity, or hue, areextracted from an image for processing by a computer.

As with most computer-vision based system, accurate segmentation is acritical step before analyzing the image. Image segmentation groupspixels within an image into regions or categories, where each region cancorrespond to an object in the image. Each pixel of a region has similarcharacteristics, or features, as other pixels in the region.

One of the simplest, and most predominant, cell segmentation approachesis intensity thresholding. In this image processing technique, global orlocal information in an image is utilized to compare the intensity ofpixel to a threshold value. If a pixel is above the threshold, it isassigned to one category. Pixels below the threshold are assigned to asecond category.

The intensity thresholding approach makes use of the assumption thatcells and non-cells (background) have starkly different intensities andcan be divided into separate categories. In practice, the illumination,color representation, and other image characteristics are dependent onthe image capture device and will differ depending on the type andquality of the capture device used. Due to these differences, theintensity of cells and non-cells can be muted and the thresholdingintensity assumption breaks down. As a result, the thresholding approachused alone gives poor segmentation results.

Instead of using the absolute intensity property alone, feature-basedsegmentation using filtering is also a common approach in cellsegmentation. In one approach, filtering makes use of additional imagecharacteristics to compare pixel intensity changes that can be used toidentify the edge, for example, of an object in the image. Cells notseparated by an edge are grouped into the same category. This approachprovides useful cues but cannot give perfect cell segmentation resultswithout further enhancements.

In addition to differential filters, which identify differences betweentwo regions of an image, morphological filters using nonlinear operatorssuch as erosion, dilation, opening and closing are also useful for cellsegmentation. This approach is useful to enhance the image structure forsegmentation by grouping neighboring pixels that have similar features.Region based segmentation using some primary knowledge or assumptionsabout initial points (seeds) and region growing is also very popular.Some common methods that use this approach are the hierarchicalsplit-and-merge and watershed methods.

Another well-known approach is based on using deformable models, whichare formulated as either implicit or explicit. Level sets, which are oneof the most popular methods in this category, are able to handletopological changes and are thus useful for cell segmentation and celltracking. However, most of the current approaches make use of globalinformation when considering the entire image as a whole and do not givemuch consideration to the special features of blood cells, e.g that twodifferent colors can be represented in the same cell, especially whiteblood cells.

Some approaches use a more targeted analysis of areas of color in acell. Color space or color modeling is defined as a model that is ableto represent color numerically in terms of three or more coordinates.Some common color spaces, such as RGB, YIQ, HSV, Lab, have beeneffectively used in many computer vision applications. However, suchcolor spaces were not particularly designed for medical images and itshows some weakness when displaying a white blood cell, as shown in FIG.1.

In FIG. 1, the first column shows the original image. The second columnshows the image adapted to the HSI color space, in which the white bloodcells are presented similarly to the background, creating littledifferentiation between the two. The third column shows the image in theRGB color space and the white blood cell is presented in a similar colorto the red blood cell, which leads to difficulty in separating the two.Hence, finding an appropriate color space for peripheral blood images topresent the white blood cells as a distinct component of the image is animportance task for pathological analysis of blood cells.

In addition to the drawbacks associated with current analysistechniques, most blood cell analysis methods and systems haveconcentrated on segmentation with the assumption that white blood cellsare already present in the peripheral blood image. These methods haveworked well on the images where white blood cells are present; however,the approaches experience difficulties when there are only red bloodcells in the image, as shown in the first two columns of FIG. 2. Forexample, when no white blood cells are present, only two regions of theimage, background and red blood cells, have to be separated. On theother hand, when white blood cells are present, three regions of theimage, background, red blood cells, and white blood cells, have to beconsidered.

Given the drawbacks of current cell segmentation techniques, it isdifficult to isolate and identify individual cells in an image. It wouldtherefore be advantageous to develop a system and method of transforminga blood smear image to provide for a clear differentiation of targetedareas, enabling accurate segmentation of individual cells. With propersegmentation of the cells, classification of characteristics ofindividual cells can be used in disease diagnosis. While one embodimentof the present invention applies to blood cell images, the invention canbe applied to images of other biologic cells.

SUMMARY OF THE INVENTION

Described herein are methods and systems that incorporate computervision and machine learning techniques for classification of biologicalcells, which can be used alone or as an aid in disease diagnostics. Moreparticularly, the present invention describes an approach comprising:(a) employing a robust and discriminative color space to transform ablood smear image, which will help aid in the segmentation of the bloodcells in the image; (b) segmenting the cells in the image, wherein theprocess can further detect if a while blood cell is present and if so,segmenting the internal components of the white blood cell; (c)characterizing the cells and other components through a combination ofdifferent type of features including shape, color, texture, andinvariant information, and (d) classifying cells by associating abnormalcell characteristics with disease states.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts the presentation of an image according to severalpre-designed color spaces and the color space of one embodiment of thepresent invention.

FIG. 2 shows images of blood cells in the top row as contrasted toexamples of cell segmentation when the peripheral blood images containsonly red blood cells or contains both red blood cells and white bloodcells, according to techniques known in the art.

FIG. 3 is a flow chart showing the method of the present inventionaccording to one embodiment.

FIG. 4 is a flowchart depicting the transformation of an image to aspecific color space for blood cells according to the present invention.

FIG. 5 is a flowchart showing the blood cell segmentation step of themethod of one embodiment of the present invention.

FIG. 6 is a flowchart showing the classification step of the method ofone embodiment of the present invention.

FIG. 7 depicts the results of the segmentation step, wherein the top rowshows the original image and the bottom row shows the transformed image.

FIG. 8 depicts the results of the classification step, wherein the toprow shows the original image and the bottom row shows the transformedimage, with certain cells labelled as abnormal.

FIG. 9 depicts the results of white blood cell detection, wherein thetop row shows the original image and the bottom row shows the same imagewith white blood cells highlighted.

FIG. 10 shows the results of segmentation on multiple examples of bloodcell images, according to one embodiment of the method of the presentinvention.

FIG. 11 shows examples of cell segmentation according to prior arttechniques (top row) and the segmentation method of the presentinvention (bottom row).

FIG. 12 shows the detection and classification of abnormal red bloodcells—schistocytes—as an output of a system according to one embodiment.

FIG. 13 shows the detection and classification of acanthocytes as anoutput of the system.

FIG. 14 shows the detection and classification of acute myeloid leukemiaas an output of the system.

FIG. 15 is a flowchart depicting the overall method of analyzing animage according to one embodiment of the present invention.

FIG. 16 is a flowchart providing additional process steps fortransforming an image to a blood cell color space.

FIG. 17 is a flowchart outlining the process of segmenting cells in animage.

FIG. 18 is a flowchart identifying the process of classifying the cells.

FIG. 19 is a block diagram of a system of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Described herein are methods and systems that utilize computer visionand machine learning techniques for classification of biological cellsas an aid in disease diagnostics. In the preferred embodiment, themethod is generally comprised of obtaining an image of blood cells;transforming the image to a color space that presents a high level ofdifferentiation between cells, the background, and components ofinterest; segmenting, or isolating, individual cells and cell structuresin the transformed image; identifying and scoring a set of features ofthe isolated cell; and classifying each isolated cell with reference toa database of known cell types based on the feature set. A flowchart ofthe basic method of the preferred embodiment is shown in FIG. 15. Moredetailed flowcharts of each step are shown in FIGS. 16-18. In addition,a graphical representation of the method is shown in FIG. 3.

Referring to FIG. 15, at step 100, obtaining an image of blood cells isaccomplished with any device capable of capturing an image containingdata of various image parameters such as color, luminosity, hue, andintensity, to name a few. The device can be a digital camera thatcaptures the image directly, or it can be a scanner that creates animage from a traditional photograph. To present the blood cells forcapture, a thin layer of blood is smeared on a microscope slide. Theblood film, or peripheral blood smear, can also be stained according totechniques known in the art.

With respect to step 200, a color space is developed and applied to theraw image to create a transformed image in a manner that highlights thedistinction between the cells, cell parts such as the nucleus, and thebackground. Color space or color modeling is a model that is able torepresent color numerically in terms of three or more coordinates. Somecommon color spaces, such as RGB, YIQ, HSV, and Lab, have beeneffectively used in many computer vision applications. However, thesecolor spaces are not particularly designed for blood cell analysis,which is represented in a very special color range.

Because known color space models are inadequate when used for blood cellimages, the system and method of the present invention utilize a colorspace developed specifically for blood cells. Referring to FIG. 16,transforming the image according to the blood cell color space iscomprised of the following: cells or regions contained in the image arelabelled at step 201; once a component or cell is labeled, features areextracted and a feature vector is created of the labelled regions atstep 202; based on the feature vector, known color modeling techniquesare applied at step 203 in which the color space is optimized totransform the image, wherein the various models are used to assign aweight to particular characteristics of the image data for furtheranalysis at step 204; and the color space is applied to the capturedimage at step 205. Optimization of the color space is accomplishedthrough machine learning techniques, where an image is compared to atraining dataset. As an example of the optimization, the RGB data in animage may be presented as 38% of the transformed image data, with othercolor spaces representing the remainder. FIG. 4 is a graphicalrepresentation of the process of deriving the blood cell color space.

By way of further detail, at step 203, the blood cell color space isbuilt upon various blood cell color modeling techniques and can be basedon the color, intensity, hue, saturation, and other imagecharacteristics. In addition, the models can include discriminant modelssuch as PCA (Principal Component Analysis), Linear Discriminant Analysis(LDA), Locality Preserving Projection (LPP), or Local FisherDiscriminant Analysis (LFDA), to name a few. Alternatively, a generativemodel such as Gaussian Mixture Model (GMM), or Naive Bayes can be used.To derive a color space for a particular capture device, free dictionarylearning is one appropriate machine learning approach for deriving ablood cell color space.

Applicant uses the term color space to denote part of a process thatenhances an image for the segmentation and classification steps.However, the term color space encompasses more than just visible light.Any features or characteristics of the cells or image data can be usedto define the “color space” if it improves the ability to segment andclassify cells.

As with other machine learning techniques, a training dataset is used tolearn properties of a known dataset and applying them to new data. Inthe present invention, the training dataset used to create the bloodcell color space consists of different types of blood cells such asnormal red blood cells, normal white blood cells, neutrophikles,shistocytes, leukemia cells, and other abnormal blood cells. In thepreferred embodiment, the training data is collected from differentsources and is captured with different image capture devices.

In order to meet the goal of the color space being independent of thedevice used to capture the image and being robust against colordependence, the feature vector, which facilitates subsequent learningsteps, can be a combination of color information, energy, entropy,gradient and histogram data extracted from selected pixels. A pixel P isselected for feature extraction if its surrounding neighbors are labeledwith the same label as the pixel P. Color information in RGB (Red GreenBlue), HSV (Hue, Saturation, Lightness), Lab (Lightness and thecolor-opponent dimensions) can be used. The energy and entropy aredefined by the difference between the central regions and itsneighboring regions.

Once the color space is defined, the original blood cell image istransformed to provide a high level of distinction between the regionsof interest in the image. As shown in FIG. 1, red blood cells and whiteblood cells have some particular characteristics that are not wellpresented in the color space of the prior works. The first four columnsof FIG. 1 show images according to various existing techniques. Incontrast, the color space of the present invention, depicted in the lastcolumn 101 of FIG. 1, shows improved contrast between different cellsand the internal components of white blood cells. For example, multiplenuclei are shown in a few of the white blood cells, which are the largercells. Moreover, the nucleus of the white blood cell is highly visiblewith respect to the cytoplasm of the cell.

In the first four columns of FIG. 1, multiple nuclei cannot be readilyobserved due to the low contrast levels. Many diseases are manifested asabnormalities in the nucleus, so it is critical to clearly present thisregion of the image. In contrast, the nucleus is barely visible in theimage of the white blood cells in the second column, which representsthe HSI color space.

After defining the color space, the cells are segmented at step 300.FIG. 17 is a flowchart depicting one embodiment of the segmentationprocess. Steps 301 and 302 relate to feature extraction to be used inconnection with segmentation algorithms. These steps can be performedseparately or as part of the prior color space feature extractionprocess.

Before segmenting the blood cells, a white blood cell detection processis performed at step 303 by scanning the entire image horizontally andvertically to generate a histogram output. The histogram of 256 bins ofeach horizontal and vertical slide is then computed. For an image thathas only red blood cells, there will be two peaks in the slide. If redblood cells and white blood cells are present, there will be threepeaks. As a result, a white blood cell is proven to be present in aperipheral blood image if three-peak slides continuously exist. Thelocation of the white blood is determined as the intersection betweenthree-peak horizontal slide and three-peak vertical slide. Using suchwhite blood cell detection, a group of mixed white blood cells caneasily be expressed. If white blood cells are detected, the white bloodcell as well as the internal structure of the cell will be segmented(steps 305 and 304, respectively).

FIG. 9 shows the results of this white blood cell detection process. Forexample, images without white blood cells detected are shown in row 901.Row 902 shows the same images, but with the white blood cells detectedand highlighted with a superimposed box. Segmenting individual whiteblood cells in a group of mixed cells allows for further analysis of theinternal structure of the cell, which can provide key markers ofdiseases such as leukemia.

After white blood cells are detected, a combination of global analysisand local analysis of cell features is used to enable segmentation ofthe cells into distinct populations at step 305. The global informationis identified based on a piecewise constant approximation which assumesimage intensity is homogeneous in each region. The local imageintensities are described by Gaussian distributions. The local fittingforce and global fitting force are complementary and are utilized indifferent manners depending on characteristics of the cell feature thatis being analyzed. For example, (1) when the contour is close to anobject boundary, the local force is used in order to attract the contourtoward the object and then stops at the boundary, and (2) when thecontour is far away from an object boundary, the global force is used toovercome the weakness of local binary fitting approach. The global andlocal fitting energy functions are defined, respectively, as:

F^(G)(c₁, c₂, ϕ) = λ₁₁∫_(Ω) (c₁ − u₀)²H(ϕ) xy + λ₁₂∫_(Ω) (c₂ − u₀)²(1 − H(ϕ))xyF^(L)(f₁, f₂, ϕ) = λ₂₁∫_(Ω) K_(σ)(f₁ − u₀)²H(ϕ) xy + λ₂₂∫_(Ω) K_(σ)(f₂ − u₀)²(1 − H(ϕ))xy

To derive a smooth contour, the zero-level set regularization is usedand defined as:

Length(ϕ) = ∫_(Ω)δ(ϕ) ∇ϕxy.

Furthermore, in order to preserve the accurate computation and stablelevel set evolution, a level set regularization term defined as

${P\; (\phi)} = {\int_{\Omega}{\frac{1}{2}\ {{{\nabla\phi} - 1}}^{2}{x}{y}}}$

is used. Thus, the energy functional is defined using four terms asfollows:

${F\left( {c_{1},{c_{2}f_{1}},f_{2},\phi} \right)} = {{\frac{\alpha}{\alpha + \beta}{F^{Global}\left( {c_{1},c_{2},\phi} \right)}} + {\frac{\beta}{\alpha + \beta}{F^{Local}\left( {f_{1},f_{2},\phi} \right)}} + {v\mspace{14mu} {{Length}\left( {\phi + {\mu \mspace{14mu} {P(\phi)}}} \right.}}}$

By making use of the advantages of both local and global information,the motion of the contour is driven by the mixed fitting force. Twocomplimentary fitting forces are needed to deal with the problem ofusing the global characteristic (intensity inhomogeneity, weak objectboundary) and the problem of utilizing the local information (initialcondition dependence). The parameters α and β can be defined by entropymaximization.

As the second part of the process, the local information is defined as acombination of two dimensional (2D) intensity histograms, GradientVector Flow, and energy features. The energy feature is constructedusing both the Gradient of Gaussian (GoG) and Laplacian of Gaussian(LoG) at different kernels. In the preferred embodiment, the 2D Gaussianis defined as

${G\left( {K_{\sigma}^{x},K_{\sigma}^{y}} \right)} = {\frac{1}{2{\pi\sigma}^{2}}{{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}.}}$

The 2D GoG operator is defined as:

${\nabla{G\left( K_{\sigma}^{x} \right)}} = {\frac{K_{\sigma}^{x}}{\sigma^{2}}\frac{1}{2{\pi\sigma}^{2}}{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}}$${\nabla{G\left( K_{\sigma}^{y} \right)}} = {\frac{K_{\sigma}^{y}}{\sigma^{2}}\frac{1}{2{\pi\sigma}^{2}}{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}}$

while the 2D LoG operators are defined as:

${\nabla{G\left( K_{\sigma}^{xx} \right)}} = {\frac{\left( K_{\sigma}^{x} \right)^{2} - \sigma^{2}}{\sigma^{4}}\frac{1}{2{\pi\sigma}^{2}}{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}}$${\nabla{G\left( K_{\sigma}^{yy} \right)}} = {\frac{\left( K_{\sigma}^{y} \right)^{2} - \sigma^{2}}{\sigma^{4}}\frac{1}{2{\pi\sigma}^{2}}{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}}$${\nabla{G\left( {K_{\sigma}^{x},K_{\sigma}^{y}} \right)}} = {\frac{K_{\sigma}^{x}K_{\sigma}^{y}}{\sigma^{4}}\frac{1}{2{\pi\sigma}^{2}}{\exp \left( \frac{- \left( {\left( K_{\sigma}^{x} \right)^{2} + \left( K_{\sigma}^{y} \right)^{2}} \right)}{2\sigma^{2}} \right)}}$

The Gradient Vector Flow (GVF) is a feature preserving diffusion ofgradient information. The GVF feature is definedV(x,y,z)=[u(x,y,z),v(x,y,z),w(x,y,z)] such that the following energyfunctions are minimized.

μ∇² u−(u−ƒ _(x))|∇ƒ|²=0, μ∇² v−(v−ƒ _(x))|∇ƒ|²=0,

μ∇² w−(w−ƒ _(x))|∇ƒ|²=0 where ∇ƒ=(ƒ_(x),ƒ_(y),ƒ_(z))

The 2D histogram of an M×N image with L gray levels (L=256 for agrayscale image) is defined as a co-occurrence matrix L×L where L is a1D histogram. For each image pixel at spatial co-ordinate (m, n), withits gray level specified by/(m, n), it considers two neighboring pixelsat locations of (m+1, n), (m, n+1). Let O_(ij) be the (i, j)^(th)element of the co-occurrence matrix,

${O_{ij} = {\sum\limits_{m = 1}^{M}{\sum\limits_{n = 1}^{N}X_{mn}}}},$

where X_(mn)=1 if I(m,n)=i and I(m+1,n)=j and I(m,n+1)=j. From the graylevel i to the gray level j, the desired transition probability is

$p_{ij} = {\left( {\sum\limits_{l_{1} = 1}^{L}{\sum\limits_{l_{2} = 1}^{L}O_{I_{1}I_{2}}}} \right)^{- 1}{O_{ij}.}}$

As previously stated, given an unknown testing image, it must bedetermined whether white blood cells are present. In alternativeembodiments, white blood cell detection is performed by dividing thetesting image into a set of regions and performing a feature extractionfor each region. The feature, which can be a combination of histogram,Histogram of Orientated Gradient (HOG), 2D directional Gabor, energy,entropy and color information, is computed for each region. The featuredistance between one region and its surroundings is then computed andused as a feature for classification. Each region is classified aseither consisting of white blood cell or not. During training, a modeland hyperplane are built using the same training data used to create theunique blood cell color space. At testing, the feature distance betweenone region and its surrounding is first computed and projected onto thehyperplane and training model, the region is then classified as a whiteblood cell or a red blood cell.

For images containing only red blood cells, the image is segmented by2-phases energy-based segmentation. For images containing both whiteblood cells and red cells (salad-mixed), the image is segmented byeither 3-phases or 4-phases energy based segmentation. The k-phasessegmentation at step 305 is chosen as the one which obtains minimumenergy. The graphical representation of the blood cell segmentation step300 is shown in FIG. 5. The k-phases segmentation step 305 is performedby repeating the 2-phases energy-based segmentation approach. Forexample, 4-phases segmentation is implemented by first employing the2-phases. For each region, the 2-phases approach is reapplied.

Some examples of cell segmentation results are shown in FIG. 7. As seenin the images in the bottom column of FIG. 7, individual cells, as wellas the nucleus of white blood cells, are isolated from other cells andthe background. FIG. 10 shows similar results of the segmentation stepfor a different set of images. FIG. 11 compares the results of thesegmentation step of the present invention in row 1102 (bottom row) andthe current state-of-the-art in row 1101 (top row), which is based ongray scale contrast enhancement and filtering. As seen in FIG. 11, thenuclei of the white blood cells are poorly defined or missed alltogether in row 1101.

Feature extraction is used throughout the method of the presentinvention. Intuitively, features related to shape information, color,and texture feature of blood cells are ideal for classification of suchcells. In addition, these features should be rotation and scaleinvariant, to make the system robust in real-world scenarios. That is,features should not be dependent on how the cells are presented orcaptured in the image.

Regarding shape identification, Fourier Descriptors are used. TheFourier Descriptor are Fourier transforms of the Centroid ContourDistance curve, which measures the distances from the blood cellboundary to the centroid.

To begin the shape identification process, the Hu geometric moments thatare invariant to rotation and scale are used. The central moments isdefined as

${M_{ij} = {\sum\limits_{x,y}\; {x^{i}y^{j}{I\left( {x,y} \right)}}}},$

where I is the blood cell image under consideration. The translationinvariant is defined as

${\mu_{pq} = {\sum\limits_{m = 1}^{p}{\sum\limits_{n = 1}^{q}{\begin{pmatrix}p \\m\end{pmatrix}\begin{pmatrix}q \\n\end{pmatrix}\left( {- \overset{\_}{x}} \right)^{({p - m})}\left( {- \overset{\_}{y}} \right)^{({q - n})}M_{mn}}}}},$

where

${\overset{\_}{x} = \frac{M_{10}}{M_{00}}},{\overset{\_}{y} = {{\frac{M_{01}}{M_{00}}\mspace{14mu} {and}\mspace{14mu} \begin{pmatrix}p \\m\end{pmatrix}} = {\frac{p!}{{m!}{\left( {p - m} \right)!}}.}}}$

The scale invariant is defined as

$\eta_{pq} = {\mu_{00}^{- {({1 + \frac{p + q}{2}})}}{\mu_{pq}.}}$

The rotation invariant is defined as

$\theta = {\frac{1}{2}{{\arctan \left( \frac{2\; \mu_{11}}{\mu_{20} - \mu_{02}} \right)}.}}$

As the next step of the shape identification process, the Zernikeorthogonal moments are used to extract the shape features of bloodcells. This method uses a set of complex polynomials, which form acomplete orthogonal set over the interior of the unit circle x²+y²=1.The form of these polynomials is V_(pq) (r,θ)=R_(pq) (r)e^(jqθ) where pis a non-negative integer, q is positive and negative integers subjectto constraints p−|q| even and |q|≦p, r is the length of vector from theorigin to the pixel (x, y), θ is the angle between vector r and x axisin count-clockwise direction. R_(pq)(r) is the radial polynomial definedas,

${R_{pq}(r)} = {\sum\limits_{s = 0}^{{({p - {q}})}/2}{\frac{{\left( {- 1} \right)^{s}\left\lbrack {\left( {p - s} \right)!} \right\rbrack}r^{p - {2s}}}{{s!}{\left( {\frac{p - {q}}{2} - s} \right)!}{\left( {\frac{p + {q}}{2} - s} \right)!}}.}}$

These polynomials are orthogonal and satisfied the orthogonalityprinciple as follows:

${{{V_{nm}^{*}\left( {x,y} \right)}.{V_{pq}\left( {x,y} \right)}}{x}{y}} = {\frac{\pi}{n + 1}\delta_{np}\delta_{mq}\mspace{14mu} {where}}$$\delta_{ab} = \left\{ {{{\begin{matrix}1 & {a = b} \\0 & {a \neq b}\end{matrix}\mspace{14mu} {and}\mspace{14mu} x^{2}} + y^{2}} = 1} \right.$

Zernike moments are the projection of the image function onto theseorthogonal basis functions. The Zernike moment of order p withrepetition q for a continuous image function ƒ(x,y) that vanishesoutside the unit circle is

${Z_{pq} = {\frac{p + 1}{\pi}{f\left( {x,y} \right)}{V_{pq}^{*}\left( {r,\theta} \right)}{x}{y}}},$

where x²+y²<1. For a digital image, the integrals are replaced bysummations:

$Z_{pq} = {\frac{p + 1}{\pi}{\sum\limits_{x,y}\; {{f\left( {x,y} \right)}{V_{pq}^{*}\left( {r,\theta} \right)}}}}$

where x²+y²<1. The shape identification will be stored in the featurevector and used in connection with the other feature calculations tocharacterize a particular cell. During feature extraction, the entireimage, image regions, blood cells, and other components are representedas a feature vector. The vector is then used in the training phase tocreate the model (or hyperplane) or in the testing phase in order toidentify the type of blood cell.

In addition to extracting the shape features for segmented blood cells,four different types of textures from a given blood cell are extracted.The texture features include color features with x²-histogram andQuaratic x histogram, 2D directional Gabor features, Histogram ofOriented Gradient (HOG), Scale Invariant Feature Transform, (SIFT),Haralick's texture, Tamura's texture, and Non-subsampled ContourletTransform features.

To extract texture features, first a new histogram distance family, theQuadratic-Chi (QC), is used. QC members are Quadratic-Form distanceswith a cross-bin 2-like normalization. The cross-bin 2-likenormalization reduces the effect of large bins having undue influence inthe overall extraction process. In many instances, normalization ishelpful, with a 2 histogram distance outperforming a L2 norm. QCutilizes two new cross bin histogram distance properties:Similarity-Matrix-Quantization-Invariance and Sparseness-Invariance,which can boost performance of the texture extraction process. QCdistances computation time complexity is linear in the number ofnon-zero entries in the bin-similarity matrix and histograms and it caneasily be parallelized.

As the next step of the texture extraction process, 2D directional Gaborfilters of varying size, frequency, and orientation are used to filterthe regions of extracted blood cells and use these filter responses inboth the real and imaginary components as features to match an unseenprobe blood cell image to a blood cell image in the given gallery. TheGabor filter is defined as a product between Gaussian function

${f\left( {x,y} \right)} = {\frac{1}{2\; {\pi\sigma}_{x}\sigma_{y}}{\exp \left( {\frac{- \left( {x - \mu_{x}} \right)^{2}}{2\; \sigma_{x}^{2}} - \frac{\left( {y - \mu_{y}} \right)^{2}}{2\; \sigma_{y}^{2}}} \right)}}$

and complex exponential sinusoid function s(x,y)=exp(j2π(u₀x+v₀y)) whereμ_(x), μ_(y), σ_(x), σ_(x) define the respective means and standarddeviations along each corresponding x and y directions and

$K = {\frac{1}{2\; {\pi\sigma}_{x}\sigma_{y}}.}$

The Gabor filter in spatial domain is defined as g(R₁, R₂, |σ_(x),σ_(y), λ, θ)=s×ƒ=K exp(−R₁ ²/2σ_(x) ²−R₂ ²/2σ_(y) ²)exp(j2π1/λR₁),includes two separated components (real and imaginary) and is defined asshown in, in which λ is the wavelength of the sinusoidal factor, θ isthe orientation of the normal to the parallel stripes of a Gabor filter,R₁=(x−μ_(x))cos θ+(y−μ_(y))sin θ, R₂=−(x−μ_(x))sin θ+(y−μ_(y))cos θ and.

Next, Histogram of Oriented Gradient (HOG) descriptor which counts thenumber of occurrences of gradient orientation in a subimage (a localizedportion of an image) is utilized. For each region (subimage), thegradient is first extracted by edge detection algorithms that are knownto a person having ordinary skill in the art. For example, in onealgorithm, the gradient magnitude m=√{square root over (G_(x) ²+G_(y)²)} and orientation

$\theta = {\arctan \left( \frac{G_{y}}{G_{x}} \right)}$

are computed, where G_(x) and G_(y) are gradient (first derivative)along x and y directions. The histograms of edge gradients withdifferent orientations (8 orientations in the preferred embodiment) arethen calculated from each subimage. In addition to HOG, Scale InvariantFeature Transform (SIFT) descriptor is another feature which also makesuse of edge and orientation information. SIFT descriptor computes thehistogram of orientation around a key point which found by a detector(SIFT detector, Harris detector). Each point is weighted by a Gaussianfunction. Coordinates of descriptors and orientations rotated tokeypoint orientation to achieve rotation invariance of the descriptor.

In the next step of the texture feature extraction, the entropy of theimage can be computed by a texture feature defined as a gray levelco-occurrence matrix. The element (i, j) of the co-occurrence matrix Mdis the number of occurrences of pixels whose gray levels are i and j,respectively and the distance between them is d, (|i−j|=d). Tamuratexture features consider three aspects of contrast (intensity differentamong neighboring pixels), coarseness (distances of notable spatialvariations of gray-level implicating the size of texels (primitiveelements) forming the texture), directionality (frequency distributionof oriented local edges against their directional angles), linelikeness(an average coincidence of the edge direction that co-occurred in thepairs whose distance is d), regularity (standard deviation of thefeature in subimage) and roughness (sum of coarseness and contrastmeasures).

As a last step, the Non-subsampled Contourlet Transform, which isdefined as a fully shift-invariant, multi-scale, and multi-directionaltransform is applied. It is constructed using a Non-subsampled Pyramid(NSP), responsible for the multi-scale information, and theNon-subsampled Directional Filter Bank (NSDFB), which is responsible forconducting the directional information. Given a segmented blood cellimage I_(i) represented at the i-th level, 1≦i≦J, where J is the highestmaximum level of the decomposition, I_(i) is divided into a sub-bandI_(i) ^((L)) and I_(i) ^((H)) by using the NSP equipped with a low-passfilter H^((L)) and a high-pass filter H^((H)) as shown in follows, inwhich * is the convolution operator. I_(i) ^((L))=H^((L))*I_(i) andI_(i) ^((H))=H^((H))I_(i), The high-pass sub-band I_(i) ^((H)) is thendecomposed into directional sub-bands by using the NSDFB, which isconstructed in cascades comprising of parallelogram filters andtwo-channel fan filter banks. The low-pass sub-band I_(i) ^((L)) is inturn used for the next decomposition. The procedure is in turn appliedto the low-pass sub-band to obtain the next level decomposition.Generally, the decomposition procedure of NSCT is formulated as shown inNSCT(I)=(I_(j) ⁰; (I_(i;k))_(i;k)) in which I is the given image, I_(j)⁰ is the low-pass sub-band and (I_(i;k))_(i;k) are directional sub-bandcoefficients.

The features extracted from the image are then used to classify eachcell in the image at step 400. Referring to FIG. 18, the classificationstep 400 is comprised of characterizing the cells based on features suchas shape, color, size, or quality of the nucleus, to name a few, at step401; next, the characterization of a cell is compared to thecharacterization of a reference cell at step 402; in turn, a cell isclassified based on the comparison at step 403.

There are a plethora of pattern recognition algorithms to employ tobiometrically model and classify blood cells. Those skilled in the artwill recognize that many such classifications systems could be used inthe present invention, including but not limited to Linear DiscriminantAnalysis (LDA), Kernel Discriminant Analysis (KDA), NeighborhoodPreserving Embedding (NPE), Orthogonal Linear Graph Embedding (OLGE),Unsupervised Discriminant Projection (UDP), Marginal Fisher Analysis(MFA), Locality Preserving Projection (LPP), Local Fisher DiscriminantAnalysis (LFDA), Convolutional Neural Network (CNN), Support VectorMachine (SVD), Kernel Correlation Feature Analysis (KCFA), and our newdevelopment, Sparse Class Dependent Feature Analysis (SCFA). A briefdescription of the pattern recognition algorithms is as follows:

LDA: aims at minimizing intra-class separation while simultaneouslymaximizing inter-class separation. In other words, LDA minimizes thewithin class scatter while between class scatter is maximized. Given aset of n samples x_(j) of classes with n_(i) samples from i^(th) classwith class label y_(i), the within class scatter matrix

$S_{w} = {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{n}\; {{A_{i,j}^{w}\left( {x_{i} - x_{j}} \right)}\left( {x_{i} - x_{j}} \right)^{T}}}}$

and the between class scatter matrix

${S_{b} = {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{n}\; {{A_{i,j}^{b}\left( {x_{i} - x_{j}} \right)}\left( {x_{i} - x_{j}} \right)^{T}}}}},{{{where}\mspace{14mu} A_{i,j}^{w}} = \left\{ {{\begin{matrix}{1/n_{c}} & \left( {y_{i} = {y_{j} = c}} \right) \\0 & \left( {y_{i} \neq y_{j}} \right)\end{matrix}{and}\mspace{14mu} A_{i,j}^{b}} = \left\{ \begin{matrix}{{1/n} - {1/n_{c}}} & \left( {y_{i} = {y_{j} = c}} \right) \\{1/n} & \left( {y_{i} \neq y_{j}} \right)\end{matrix} \right.} \right.}$

The optimal solution which is found by solving the LDA criterion is

$\phi = {\arg \mspace{11mu} {\max\limits_{\phi}{\left( {{tr}\frac{\phi^{T}S_{b}\phi}{\phi^{T}S_{w}\phi}} \right).}}}$

LPP: aims at decreasing the distance between nearby samples in theoriginal space and does not take between class separability intoaccount. In this method, the locality matrix

${S_{l} = {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{n}{{A_{i,j}^{l}\left( {x_{i} - x_{j}} \right)}\left( {x_{i} - x_{j}} \right)^{T}}}}},$

where A_(i,j) ^(l)=exp(−∥x_(i)−x_(j)∥²). The LPP objective function isdefined as

${{\min\limits_{\phi}{\left( {{tr}\left( {\phi^{T}S_{l}\phi} \right)} \right)\mspace{14mu} {s.t.\mspace{14mu} \phi^{T}}{XDX}^{T}\phi}} = I},$

where D is an n-dimensional diagonal matrix with its i^(th) diagonalelement defined as

$D_{i,i} = {\sum\limits_{j = 1}^{n}{A_{i,j}^{l}.}}$

LFDA: aims to maximize the between-class separability while within classmultimodality is preserved. The method is qualified by three criticalconditions: nearby samples in the same class are made close, far apartsamples in the same class are separated, and samples in differentclasses are separated. In this method, the local within-class scattermatrix

${\overset{\sim}{S}}_{w} = {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{n}{{{\overset{\sim}{A}}_{i,j}^{w}\left( {x_{i} - x_{j}} \right)}\left( {x_{i} - x_{j}} \right)^{T}}}}$

and the local between class scatter matrix

${{\overset{\sim}{S}}_{b} = {\frac{1}{2}{\sum\limits_{i,{j = 1}}^{n}{{{\overset{\sim}{A}}_{i,j}^{w}\left( {x_{i} - x_{j}} \right)}\left( {x_{i} - x_{j}} \right)^{T}}}}},$

where

$A_{i,j}^{w} = \left\{ {{\begin{matrix}{A_{i,j}^{l}/n_{c}} & \left( {y_{i} = {y_{j} = c}} \right) \\0 & \left( {y_{i} \neq y_{j}} \right)\end{matrix}\mspace{14mu} {and}{\overset{\sim}{A}}_{i,j}^{b}} = \left\{ {\begin{matrix}{A_{i,j}^{l}\left( {{1/n} - {1/n_{c}}} \right)} & \left( {y_{i} = {y_{j} = c}} \right) \\{1/n} & \left( {y_{i} \neq y_{j}} \right)\end{matrix}.} \right.} \right.$

The solution to the optimization problem

$\phi^{*} = {\arg \; {\max\limits_{\phi}\left( {{tr}\; \frac{\phi^{T}{\overset{\sim}{S}}_{b}\phi}{\phi^{T}{\overset{\sim}{S}}_{w}\phi}} \right)}}$

is {tilde over (S)}_(b)φ=λ{tilde over (S)}_(w)φ.

SVM: aim to compute a hyper-plane in the feature space with a decisionboundary w^(T)x+c=0 that maximizes the margin

$\frac{2}{w}$

between the training samples of each class (denoted demarcated by thelines w^(T)x+c=−1 and w^(T)x+c=+1). The constrained maximum margin canbe derived and reformulated as a constrained convex optimizationproblem:

$\min\limits_{w,c}{\frac{1}{2}w^{T}w}$

s.t y_(i)(w^(T)x_(i)+c)≧1. The primal optimization problem in the aboveequation for the linearly separable SVM can be redefined with its dualequivalent optimization problem as

${\min\limits_{\alpha}{\frac{1}{2}\alpha \times {{diag}(y)} \times K \times {{diag}(y)} \times \alpha}} - {e \times \alpha}$

s.t. α_(i)>0∀iε[1,N] and y^(T)α=0, where K is the kernel[K_(i,j)]=[φ(x_(i))·φ(x_(j))] where φ(x_(i))=x_(i) for linear SVM, e isa vector of ones 1, and diag(y) is a diagonal matrix with y on itsdiagonal. In kernel SVM, the function φ is defined such that it maps thedata into a higher dimensional space where a SVM linear decisionboundary is computed. When this linear decision boundary is mapped backinto its original feature space, this boundary is distinctly non-linear.

KCFA: The correlation output of test image y with filter h:y⁺h=y⁺[T⁻¹X(X⁺T⁻¹ X)⁻¹ u] or y⁺h=(({tilde over (y)}+{tilde over(X)}))(({tilde over (X)})+{tilde over (X)})⁻¹u where h=T⁻¹X(X⁺T⁻¹ X)⁻¹u,{tilde over (X)}=T^(−1/2)X and {tilde over (Y)}=T^(−1/2)y denote thepre-whitened version of X and y. Using the kernel trick yields thekernel correlation filter with mapping:

φ(y)·φ(h)=(φ(y)·φ(X))(φ(X)·φ(X))⁻¹ u=K(y,x _(i))K(x _(i) ,x _(j))⁻¹ u

CNN: Instead of using templates, CNN is used in order to automaticallyextract local feature. One CNN consists of many layers, each layer playsa feature extraction role and performs different operators such asconvolutions, subsampling, pooling, full connection, etc. Similar toother NN, CNN is trained by backpropagation. Based on performance,online error backpropagation is used in general. The learning process isan iterative procedure where the weights are updated by a small step inthe opposite direction of the steepest gradient ∇E at each iteration.The error function of K output is simply defined as

${E_{p} = {\frac{1}{2}{\sum\limits_{k = 1}^{K}\left( {o_{p\; k} - t_{p\; k}} \right)^{2}}}},$

where o and t are output of neuron and target value, respectively. Moreproductive, the error can defined by cross-entropy. The weight updatingrule from neuron i to neuron j in the layer l is

$\left. w_{ij}^{l}\leftarrow{w_{ij}^{l} + {\lambda \; {\frac{\partial E_{p}}{\partial w_{ij}^{l}}.}}} \right.$

The hidden units use tan h active function and the outputs use thesoftmax function.

SCFA: While the foregoing approaches can provide fairly accurateresults, a novel approach named Sparse Class-dependent Feature Analysis(SCFA) is used in the preferred embodiment of the present invention.SCFA is used to combine the advantages of sparse representation in anover complete dictionary (K-SVD for instance), with a powerfulnon-linear classifier. The classifier is based on the estimation ofclass-specific optimal filters, by solving an L1-norm optimizationproblem which is solved using the Alternating Direction Method ofMultipliers (ADMM). In ADMM, the system solves

${\min\limits_{h}{\frac{1}{2}{{{{\overset{\sim}{X}}^{T}h} - u}}_{2}^{2}}} + {\lambda {z}_{1}}$

s.t Fh−z=0 instead of using LASSO solver

${\min\limits_{h}{\frac{1}{2}{{{{\overset{\sim}{X}}^{T}h} - u}}_{2}^{2}}} + {\lambda {{{Fh}}_{1}.}}$

The corresponding augmented Lagrangian form

${{{is}\mspace{14mu} {L_{\rho}\left( {h,z,y} \right)}} = {{\min\limits_{h}{\frac{1}{2}{{{{\overset{\sim}{X}}^{T}h} - u}}_{2}^{2}}} + {\lambda {z}_{1}} + {\rho \; {y^{T}\left( {{Fh} - z} \right)}} + {\frac{\rho}{z}{{{Fh} - z}}^{2}}}},$

where y is the augmented Lagrange multiplier and ρ>0.

FIG. 6 shows a graphical representation of the proposed blood cellclassification process. Examples of blood cell classification, withvarious abnormal cells positively identified among a group of normalcells, are shown in FIG. 8.

The foregoing has described various embodiments of the method of thepresent invention. A representation of the system embodying thesemethods is shown in FIGS. 12-14 and 19. Referring to FIG. 19, in thepreferred system, the process steps thus described will be carried-outby a computer 1901 or other processor capable of executing softwareperforming the feature extraction and modeling steps. The system willpresent a visual representation of the transformed image on a display1902, with abnormal cells or other regions of interest highlighted forfurther analysis by a trained pathologist. FIG. 19 further shows animage capture device 1903 that generates an image and sends the imagedata to computer 1901.

Alternatively, the results of the classification step can be presentedin a report. Unlike a visual classification performed by a pathologist,the result can further include a quantitative assessment. For example,the report can indicate that the nucleus of a white blood cell occupies63% of the cell, which is near a threshold for positively identifying adisease. With this level of analysis, a person who is borderline sickcan schedule follow-up visits to ensure an abnormality has notprogressed to a full-blown disease.

Those skilled in the art will recognize that the use of the describedmethods and systems to classify cells can be readily used as a tool fordisease diagnostics with other types of cells. Given the machinelearning aspects of the invention, the color space, feature extraction,and classification processes can be adapted to other types of cells withan appropriate learning dataset.

While the disclosure has been described in detail and with reference tospecific embodiments thereof, it will be apparent to one skilled in theart that various changes and modifications can be made therein withoutdeparting from the spirit and scope of the embodiments presented. Thus,it is intended that the present disclosure cover the modifications andvariations of this disclosure provided they come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A method of analyzing biological cells, comprising: obtaining an image of a plurality of cells; transforming the image according to a cell color space, wherein the cell color space provides differentiation between the plurality of cells and a background; segmenting individual cells within the plurality of cells; and classifying the individual cells.
 2. The method of claim 1, wherein transforming the image according to a cell color space further comprises: labelling a region of the image; extracting features from the region to create a feature vector; using the feature vector, applying modeling techniques; based on the modeling techniques, defining the cell color space; and applying the cell color space to the image.
 3. The method of claim 2, further comprising: using a training dataset to optimize the cell color space.
 4. The method of claim 1, wherein segmenting individual cells of the plurality of cells comprises: identifying features of a region of the image; extracting the features of the region; labelling a region as the individual cell or a background based on the features; and isolating the individual cells in the image.
 5. The method of claim 1, wherein classifying the individual cells comprises: characterizing the individual cells based on cell features; comparing the characterization of the individual cells to a characterization of a reference cell; and classifying the individual cells based on the comparison to the reference cell.
 6. The method of claim 5, wherein the reference cell is selected from the group consisting of normal red blood cells, normal white blood cells, abnormal red blood cells, abnormal white blood cells, neutrophikles, shistocytes, and leukemia cells.
 7. The method of claim 1, wherein the plurality of cells are blood cells.
 8. The method of claim 4, further comprising: based on the features, detecting a presence of white blood cells within the plurality of cells.
 9. The method of claim 1, wherein the image contains data used to define the color space.
 10. The method of claim 9, wherein the data comprises at least one of the following: red, green, and blue color information; hue, saturation, and lightness data; lightness and color-opponent dimensions; energy; and entropy.
 11. A cell classification system, comprising: an image capture device for acquiring an image of cells, wherein the image capture device provides an output containing image data; a device for receiving the output and creating a transformed image based on a color space, segmenting a plurality of individual cells within the image based on the color space, characterizing a first cell of the plurality of individual cells, classifying the first cell as normal or abnormal based on the characterization; and a display for visually representing the transformed image.
 12. The system of claim 11, wherein the device is a computer.
 13. A method of classifying a blood cell among a plurality of blood cells in an image, the method comprising: extracting image data from an image of a plurality of blood cells; partitioning the image into a set of distinct regions, wherein a first region of the set of distinct regions contains similar pixels; identifying a feature set from the first region, wherein the feature set is based on the image data; defining a cell color space for the first region, wherein the color space is derived from at least one color modeling technique; optimizing the color space by using a training dataset applied in a machine learning process; transforming the image using the optimized color space; partitioning the transformed image into a second set of distinct regions, wherein a second region of the second set of distinct regions contains similar pixels; extracting features from the second region to create a feature vector, wherein the feature vector is based on transformed image data; detecting whether a white blood cell is present in the second region; performing at least one iteration of segmentation; creating segmentation of individual cells based on the iterations of segmentation; classifying individual cells based on the feature vector, wherein the feature vector is compared to a reference feature vector created from a group of reference cells.
 14. The method of claim 13, wherein the machine learning process is a free dictionary learning technique.
 15. The method of claim 13, wherein performing at least one iteration of segmentation is repeated until an energy is minimized.
 16. The method of claim 13, wherein the features comprise at least one of a shape, color, and texture of the individual cells.
 17. The method of claim 13, wherein classifying individual cells is accomplished by executing a sparse class-dependent feature analysis algorithm on the feature vector. 